Saying something irrelevent to the conversation.
Perhaps for fun, or to change the subject.
But there is no reason for saying something random.
It usually makes Brianne feel stupid when something's random.

ME: "ASDFKLJ"
YOU: "what was the meaning of that?"
ME: "there was none, it was random."

Random is a term used for something which is very out of the blue, like when there is a big silence and then somebody says a 'random' word, which would normally not be at all funny, and then starts uncontrolable laughing.